Keep in mind that no system is frictionless. We are assuming real systems, and the conveyer as described is well within present capabilities. It can be built.

I am keen to see someone build one. The total thrust from a 747's engines is about 250,000 pounds. That's 250,000 pounds of horizontal force applied to the center of mass of the airplane (more or less). In order to stop the plane from moving, the conveyor belt needs to apply an equal force in the opposite direction—and it can do it only by rubbing itself against the free-wheeling wheels. The conveyor belt would need to move at ungodly speeds; the tires would melt, the bearings would seize (which would, granted, help the belt out), the landing gear would snap off, and eventually the plane itself would be reduced to scrap.

This is something like trying to keep a freight train from moving forward by applying a belt sander to one side of the engine. It's theoretically possible, sure, with a magic belt sander and an impervious train, but there's no way you could build such a critter.

I think it's much more likely that the question is asking about the plane's speed relative to the ground. It doesn't make sense to me to say the speed of the belt is "exactly the same" as the speed of the plane when the speed of the belt would have to be much much faster than the plane's top speed could ever be (~600 mph for a 747). The belt is no longer matching the plane's speed, in this thought experiment; it's moving fast enough that friction prevents the plane from moving, which is not the same thing.